Z-domain counterpart to prony´s method for exponential-sinusoidal decomposition

Prony´s method has applications in exponential sinusoidal modelling, parametric modelling, filter design, system modelling and system identification. Similarly to Pade´ approximation, Prony´s method and refinements thereof are major tools for statistical signal analysis, system auto-regressive moving average (ARMA) modelling and least-squares digital filter design. In this study, a z-domain counterpart to Prony´s method is proposed as a spectral analysis approach to exponential-sinusoidal decomposition in the presence of noise contamination. The approach is particularly effective in the case where the signal components have ´well behaved´ frequencies, meaning that they are multiples of the fundamental frequency. Spectral weighting is applied to power spectra over the z-plane. Spectral peaks of signals contaminated by noise are used to estimate the amplitude, frequency, damping and phase of damped sinusoidal components. The present approach requires no a priori knowledge of the number of damped sinusoidal components present in the contaminated signal, and hence no knowledge of the system order. As expected, however, the analysed signal duration should be long enough to reveal signal properties in the presence of noise. In the case where signal components are not well behaved, spectral leakage would necessitate windowing and higher resolution frequency analysis in order to identify the successive components with improved accuracy.